González Poot and McGinnis (2006): Local versus Long-Distance Fission in Distributed Morphology

[GPMcG06]'s argument that Yucatec Maya has local but not long-distance Fission. The verbal agreement suffixes come from one node, Agr3, which agrees with both the ergative subject and the nominative object and is realized by strict scansion of the Vocabulary (27) with local Fission ([Hal97a]): an item discharges its features from one of the node's two matrices and the residue stays available to the items below (suffixes). The second- and third-person plural suffixes -éːš and -oʔob are unspecified for case, so their order is fixed by specificity whatever the grammatical roles, (19) to (22), and one scansion never inserts -oʔob twice, (23) and (24) (suffixes_rows), whereas the object–subject template (18) predicts exactly the starred forms (template_rows). Long-distance Fission is rejected: the split of ergative person onto the auxiliary and number onto the verb, (39), crosses a word boundary, and first-person number is a person distinction, (42), so the auxiliary and prefix Vocabularies (43) and (44) recover every row (aux_prefix_rows) and derive the paradigm (39) that the paper aligns with Hebrew, Basque, and Georgian (ergative_paradigm, first_person_paradigm). The appendix's privative implementation over [HR02]'s features, (A1) to (A4), recovers the auxiliary and the prefix (privative_aux_prefix) but not the suffixes: without negative values, the nominative residue of a second-person plural object still matches -en, so (A4) over-generates on (20) (privative_suffixes).

Implementation notes

The person features of (26), [±PSE, ±Auth], are the substrate's [±participant, ±author] decomposition, and [±Pl] a binary feature value. Agr3's list (27) needs the nominative first-person plural to carry [+PSE] and the singular not to, the reverse of the assignment (42) gives the ergative auxiliary; the paper does not reconcile the two, so matrix follows (27) for nominative first person and (42) otherwise. The elsewhere -Ø is inserted but not counted among a row's overt suffixes.

References

• [GPMcG06]
• [Hal97a]
• [Noy92]
• [HM93]
• [HR02]

Features and matrices, sections 3 to 5

def GonzalezPootMcGinnis2006.personFeatures (p : Person) : List Minimalist.FeatureVal

The person features of (26), [±PSE, ±Auth], as the substrate's [±participant, ±author] decomposition of a person.

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def GonzalezPootMcGinnis2006.number (pl : Bool) : Minimalist.FeatureVal

Number as the feature [±Pl].

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• GonzalezPootMcGinnis2006.number pl = ⟨Minimalist.FeatureType.number, if pl = true then Number.plural else Number.singular⟩

def GonzalezPootMcGinnis2006.ergMatrix : Person → Bool → List Minimalist.FeatureVal

In an ergative argument's matrix (42), first-person number is a person distinction, singular [+PSE, +Auth] and plural [+Auth].

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• GonzalezPootMcGinnis2006.ergMatrix Person.first false = [⟨Minimalist.FeatureType.participant, true⟩, ⟨Minimalist.FeatureType.author, true⟩, ⟨Minimalist.FeatureType.case, Case.erg⟩]
• GonzalezPootMcGinnis2006.ergMatrix Person.first true = [⟨Minimalist.FeatureType.author, true⟩, ⟨Minimalist.FeatureType.case, Case.erg⟩]
• GonzalezPootMcGinnis2006.ergMatrix x✝¹ x✝ = GonzalezPootMcGinnis2006.personFeatures x✝¹ ++ [GonzalezPootMcGinnis2006.number x✝, ⟨Minimalist.FeatureType.case, Case.erg⟩]

def GonzalezPootMcGinnis2006.matrix : Person → Bool → Case → List Minimalist.FeatureVal

An argument's matrix for Agr3 is (42) for ergative arguments and for second and third person, and for nominative first person the one the assignment (27) presupposes, -oʔon 1pl [+PSE, +Auth, NOM] and -en 1sg [+Auth, NOM].

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• GonzalezPootMcGinnis2006.matrix Person.first false Case.nom = [⟨Minimalist.FeatureType.author, true⟩, ⟨Minimalist.FeatureType.case, Case.nom⟩]
• GonzalezPootMcGinnis2006.matrix Person.first true Case.nom = [⟨Minimalist.FeatureType.participant, true⟩, ⟨Minimalist.FeatureType.author, true⟩, ⟨Minimalist.FeatureType.case, Case.nom⟩]
• GonzalezPootMcGinnis2006.matrix x✝¹ x✝ Case.erg = GonzalezPootMcGinnis2006.ergMatrix x✝¹ x✝
• GonzalezPootMcGinnis2006.matrix x✝² x✝¹ x✝ = GonzalezPootMcGinnis2006.personFeatures x✝² ++ [GonzalezPootMcGinnis2006.number x✝¹, ⟨Minimalist.FeatureType.case, x✝⟩]

The Vocabularies (27), (43), (44)

def GonzalezPootMcGinnis2006.agr3 : List (DistributedMorphology.VocabularyItem Minimalist.FeatureVal String)

The Agr3 Vocabulary Items (27), in scansion order.

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def GonzalezPootMcGinnis2006.agr1 : List (DistributedMorphology.VocabularyItem Minimalist.FeatureVal String)

The Agr1 Vocabulary Items (43) realize the ergative auxiliary suffix.

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def GonzalezPootMcGinnis2006.agr2 : List (DistributedMorphology.VocabularyItem Minimalist.FeatureVal String)

The Agr2 Vocabulary Items (44) realize the ergative verbal prefix.

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def GonzalezPootMcGinnis2006.suffixes (subj : Person × Bool) (obj : Option (Person × Bool)) : List String

In the overt verbal suffixes of a clause, Agr3 bears the subject's matrix and, in a transitive clause, the object's, (25) and (28b); strict scansion of (27) realizes them, and the elsewhere -Ø is not overt.

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def GonzalezPootMcGinnis2006.aux (subj : Person × Bool) : Option String

The auxiliary suffix of an ergative subject, by the Subset Principle over (43).

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• GonzalezPootMcGinnis2006.aux subj = DistributedMorphology.subsetPrinciple GonzalezPootMcGinnis2006.agr1 ↑(GonzalezPootMcGinnis2006.ergMatrix subj.1 subj.2)

def GonzalezPootMcGinnis2006.verbPrefix (subj : Person × Bool) : Option String

The verbal prefix of an ergative subject, by the Subset Principle over (44).

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• GonzalezPootMcGinnis2006.verbPrefix subj = DistributedMorphology.subsetPrinciple GonzalezPootMcGinnis2006.agr2 ↑(GonzalezPootMcGinnis2006.ergMatrix subj.1 subj.2)

def GonzalezPootMcGinnis2006.templateSuffixes (subj obj : Person × Bool) : List String

The rival template (18) has object agreement then subject agreement, each a node of its own realized by the Subset Principle over (27).

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The data pool: (3) to (8), (16), (19) to (24)

structure GonzalezPootMcGinnis2006.Row : Type

A row of the pool records the arguments, the auxiliary suffix, the verbal prefix, the overt verbal suffixes, and the judgment.

• subj : Person × Bool
• obj : Option (Person × Bool)
• aux : String
• verbPrefix : String
• suffixes : List String
• judgment : Judgment

@[instance_reducible]

instance GonzalezPootMcGinnis2006.instDecidableEqRow : DecidableEq Row

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• GonzalezPootMcGinnis2006.instDecidableEqRow = GonzalezPootMcGinnis2006.instDecidableEqRow.decEq

def GonzalezPootMcGinnis2006.instDecidableEqRow.decEq (x✝ x✝¹ : Row) : Decidable (x✝ = x✝¹)

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@[instance_reducible]

instance GonzalezPootMcGinnis2006.instReprRow : Repr Row

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• GonzalezPootMcGinnis2006.instReprRow = { reprPrec := GonzalezPootMcGinnis2006.instReprRow.repr }

def GonzalezPootMcGinnis2006.instReprRow.repr : Row → ℕ → Std.Format

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def GonzalezPootMcGinnis2006.Row.ofDatum (ex : Datum) : Option Row

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theorem GonzalezPootMcGinnis2006.row_ofDatum_isSome (ex : Datum) : ex ∈ Examples.all → (Row.ofDatum ex).isSome = true

def GonzalezPootMcGinnis2006.rows : List Row

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• GonzalezPootMcGinnis2006.rows = List.filterMap GonzalezPootMcGinnis2006.Row.ofDatum GonzalezPootMcGinnis2006.Examples.all

theorem GonzalezPootMcGinnis2006.suffixes_rows (r : Row) : r ∈ rows → (r.judgment = Judgment.acceptable ↔ suffixes r.subj r.obj = r.suffixes)

Under Local Fission, (19) to (24), a row is grammatical iff its overt verbal suffixes are what strict scansion of (27) inserts, -éːš before -oʔob in both (20) and (22) and -oʔob once in (24).

theorem GonzalezPootMcGinnis2006.template_rows : (∀ r ∈ rows, ∀ o ∈ r.obj, r.judgment = Judgment.ungrammatical → templateSuffixes r.subj o = r.suffixes) ∧ ∃ r ∈ rows, r.judgment = Judgment.acceptable ∧ ∃ o ∈ r.obj, templateSuffixes r.subj o ≠ r.suffixes

The template (18) predicts every starred form, -oʔob-éːš for (21) and -oʔob-oʔob for (23), and fails the grammatical (22) and (24), whose orders it reverses or doubles.

theorem GonzalezPootMcGinnis2006.aux_prefix_rows (r : Row) : r ∈ rows → aux r.subj = some r.aux ∧ verbPrefix r.subj = some r.verbPrefix

Agr1 (43) and Agr2 (44) recover the auxiliary suffix and verbal prefix of every row, (17) and (39).

Against long-distance Fission, section 5

theorem GonzalezPootMcGinnis2006.ergative_paradigm (p : Person) (h : p = Person.second ∨ p = Person.third) : aux (p, false) = aux (p, true) ∧ verbPrefix (p, false) = verbPrefix (p, true) ∧ suffixes (p, false) none = [] ∧ suffixes (p, true) none ≠ []

In the paradigm (39) for second and third person, the auxiliary suffix and the prefix mark person alone, and plurality is a verbal suffix, the distribution of (36) to (38).

theorem GonzalezPootMcGinnis2006.first_person_paradigm : aux (Person.first, false) ≠ aux (Person.first, true) ∧ ∀ (pl : Bool), suffixes (Person.first, pl) none = []

In the paradigm (39) for first person, the auxiliary distinguishes singular from plural and no verbal suffix marks number, since (42) makes first-person number a person distinction, (3) and (4).

The appendix: a privative implementation

inductive GonzalezPootMcGinnis2006.Privative : Type

[HR02]'s privative features, with the case feature the appendix adds.

• participant : Privative
• speaker : Privative
• addressee : Privative
• group : Privative
• nom : Privative

@[instance_reducible]

instance GonzalezPootMcGinnis2006.instDecidableEqPrivative : DecidableEq Privative

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• GonzalezPootMcGinnis2006.instDecidableEqPrivative x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def GonzalezPootMcGinnis2006.instReprPrivative.repr : Privative → ℕ → Std.Format

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@[instance_reducible]

instance GonzalezPootMcGinnis2006.instReprPrivative : Repr Privative

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• GonzalezPootMcGinnis2006.instReprPrivative = { reprPrec := GonzalezPootMcGinnis2006.instReprPrivative.repr }

def GonzalezPootMcGinnis2006.privMatrix (p : Person) (pl : Bool) (c : Case) : List Privative

The specifications (A1), with nominative case on a nominative argument.

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• GonzalezPootMcGinnis2006.privMatrix Person.first false c = [GonzalezPootMcGinnis2006.Privative.participant] ++ if c = Case.nom then [GonzalezPootMcGinnis2006.Privative.nom] else []
• GonzalezPootMcGinnis2006.privMatrix p false c = [] ++ if c = Case.nom then [GonzalezPootMcGinnis2006.Privative.nom] else []
• GonzalezPootMcGinnis2006.privMatrix p true c = [GonzalezPootMcGinnis2006.Privative.group] ++ if c = Case.nom then [GonzalezPootMcGinnis2006.Privative.nom] else []

def GonzalezPootMcGinnis2006.agr1' : List (DistributedMorphology.VocabularyItem Privative String)

The Agr1 Vocabulary Items (A2).

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def GonzalezPootMcGinnis2006.agr2' : List (DistributedMorphology.VocabularyItem Privative String)

The Agr2 Vocabulary Items (A3).

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def GonzalezPootMcGinnis2006.agr3' : List (DistributedMorphology.VocabularyItem Privative String)

The Agr3 Vocabulary Items (A4).

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def GonzalezPootMcGinnis2006.suffixes' (subj : Person × Bool) (obj : Option (Person × Bool)) : List String

The overt verbal suffixes under (A4).

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theorem GonzalezPootMcGinnis2006.privative_aux_prefix (r : Row) : r ∈ rows → DistributedMorphology.subsetPrinciple agr1' ↑(privMatrix r.subj.1 r.subj.2 Case.erg) = aux r.subj ∧ DistributedMorphology.subsetPrinciple agr2' ↑(privMatrix r.subj.1 r.subj.2 Case.erg) = verbPrefix r.subj

The privative Agr1 and Agr2 lists (A2) and (A3) recover the auxiliary suffix and the verbal prefix of every row.

theorem GonzalezPootMcGinnis2006.privative_suffixes : suffixes' (Person.third, true) (some (Person.second, true)) = ["éːš", "en", "oʔob"] ∧ ∃ r ∈ rows, r.judgment = Judgment.acceptable ∧ suffixes' r.subj r.obj ≠ r.suffixes

The privative Agr3 list (A4) fails a grammatical row: in (20) the object's residue after -éːš is [Participant, NOM], which -en matches, where the binary [−Auth] of (27) blocks it.